But Ms. Tymoshenko, making her first public appearance since losing the election on Sunday, did not say anything about bowing out, and her aides continued to charge that the voting was tainted by fraud.

The White House released a statement saying that Mr. Obama had called Mr. Yanukovich, the Ukrainian opposition leader, and wished him “success in carrying out his mandate.”

“This peaceful expression of the political will of Ukrainian voters is another positive step in strengthening democracy in Ukraine,” the statement said.

Ukraine has been the site of a struggle for influence between Russia and the West in recent years, and Mr. Yanukovich is considered closer to the Kremlin than Ms. Tymoshenko is. Mr. Obama’s decision to congratulate Mr. Yanukovich therefore seemed a blow to any plans by Ms. Tymoshenko to contest the election.

Even so, Ms. Tymoshenko’s aides have issued a stream of accusations this week insisting that fraud was rampant.

“We do not understand the conclusions of the international observers that the election occurred honestly and democratically,” said Sergey Paskhalov, an official from her party. “We categorically disagree with this.”

Ms. Tymoshenko is in a complicated position if she wants to discredit the election observers’ reports. When she helped lead the 2004 Orange Revolution, which overturned a presidential election won by Mr. Yanukovich that was deemed fraudulent, she cited findings of the same observers to bolster her arguments.

This week, Mr. Yanukovich appealed to Ms. Tymoshenko to bow out, saying that she was causing more instability in a country that has had no shortage of it in recent years. He also said she should resign as prime minister, rather than force him to assemble a coalition in Parliament to oust her.

But on Thursday, one of her aides, Oleksandr Turchynov, a first deputy prime minister, said she would not step down, expressing skepticism that Mr. Yanukovich would be able to gather enough support for her dismissal.